DLMF:5.9.E8 (Q2097)

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DLMF:5.9.E8
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    Statements

    Defining formula
    Γ ⁡ ( 1 + 1 n ) ⁢ cos ⁡ ( π 2 ⁢ n ) = ∫ 0 ∞ cos ⁡ ( t n ) ⁢ d t , Euler-Gamma 1 1 𝑛 𝜋 2 𝑛 superscript subscript 0 superscript 𝑡 𝑛 𝑡 {\displaystyle{\displaystyle\Gamma\left(1+\frac{1}{n}\right)\cos\left(\frac{% \pi}{2n}\right)=\int_{0}^{\infty}\cos\left(t^{n}\right)\mathrm{d}t,}}
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    DLMF id
    DLMF:5.9.E8
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    constraint
    n = 2 , 3 , 4 , … 𝑛 2 3 4 … {\displaystyle{\displaystyle n=2,3,4,\dots}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
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    Q11274
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1adec
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